Quantum particle production due to an expanding universe is a straightforward consequence of quantum field theory in curved space-time [1]}, [2]}. This effect is of special interest in the early Universe. On one hand, during Inflation, it is believed to give rise to quantum fluctuations leaving an imprint in the temperature anisotropies and polarization pattern of the cosmic microwave background. On the other hand, any inflationary model has to end with a period where all the matter and radiation that populates the actual Universe is produced, also called reheating. During this period particle production due to a background field is non negligible [3]}, [4]}. At the classical level, models like Chaotic Inflation [5]}, New Inflation [6]} or Starobinsky inflation [7]} assume a slowly moving scalar field that behaves as a cosmological constant term. After inflation, the scalar field falls down the potential and due to couplings between this scalar field and the quantized fields it can generate important amounts of particle species, including scalar [3]} and Dirac fields [9]}. A more complete description of these effects include the computation of the stress-energy tensor and the two point function in order to account for the transferred energy from the scalar field to the quantized field and to take into account possible backreaction effects via semiclassical equations.
